Circuitous Route

Piano étude: Circuitous Route (2017)
for piano (3′)

Though short, this piece is probably the most technically complicated music I have ever written. In general, it is inspired by Ligeti’s piano études, especially the 13th etude, “L’escalier du diable “. It is based on a few ideas:

Melodically, most of the material is based on a short cell: A, D♯, G, C♯, F, B, C, F♯, B♭, … or its transposition or inversion. This cell slowly climbs higher-and-higher though its voice-leading is mostly descending. The only music that does not come out of it is the chromatically descending lines in mm. 6–8, 12–13, and 51–56.

Rhythmically and formally, the music is based on the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, …). The ratios of the terms in this sequence approaches the golden ratio 1.618… (1, 2, 1.5, 1.667, 1.6, 1.625, …). Visually, you can tell that notes are grouped into groups of 2 and 3 (both Fibonacci numbers) in each bar and the bars all contain 13 or 8 (also Fibonacci numbers) eighth-notes. Less obvious is the lengths of the piece’s three sections:

1. Section A (mm. 1–21) has 233 eight-notes,

2. Section B (mm. 22–42) also has 233 eighth-notes

3. Section C (mm. 43–56) has 144 eighth-notes plus a fermata

4. At the end, there is a two-measure codetta

These lengths, 233, 233, and 144, are themselves Fibonacci numbers and add up to 610, another Fibonacci number. All of these additions are possible because of the way the Fibonacci sequence is constructed.

The harmony of the piece is result of independent lines. Because of the melodic cell the piece is based on, it has the same pure, harmonically ‘neutral’ feeling of many of Ligeti’s piano études. While writing this etude, I found that in this type of post-tonal music, you can create a sense of development with regard to harmony by making the harmony thicker-and-thicker as time passes.